Question

The explicit rule for a sequence is given.
an=−2n+7
What is the recursive rule for the sequence?
a1=7; an=an−1+2
a1=5; an=an−1−2
a1=−2; an=an−1+7
a1=7; an=an−1−2

Answer 1

As is often the case with multiple-choice questions, you can choose the correct answer by seeing if they are consistent with the problem statement.

an = -2n +7
means that the value of a1 can be found from
a1 = -2*1 +7
a1 = 5

Only one of the choices matches this condition: the correct one.

The 2nd selection is appropriate.

_____
If you want to actually work the problem, you find a[1] as above. Then, consider
.. a[n+1] = -2*(n+1) +7
.. = (-2n +7) -2 . . . . . . note the stuff in parentheses matches the definition of a[n]
.. = a[n] -2
This is also true for the previous pair of terms:
.. a[n] = a[n -1] -2

So, now you have
.. a[1] = 5
.. a[n] = a[n-1] -2
which matches the second selection.

Answer 2

Answer:

a1 = 5 ;  an = an−1 − 2

I just took the test! This is the correct answer for this problem! Good luck!